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<p>Consider</p>
<div class="displaymath process-math" data-contains-math-knowls="./knowl/eq1_6.html">
\begin{equation}
\frac{\textrm{d} y}{\textrm{d} x}=f(x, y),\tag{1.3.1}
\end{equation}
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<p class="continuation">where <span class="process-math">\(f(x, y)\)</span> is given. Suppose that the solution is given as <span class="process-math">\(y=\phi(x)\text{.}\)</span> Geometrically, it represents a curve in the <span class="process-math">\(x-y\)</span> plane. <span class="process-math">\(\frac{\textrm{d} y}{\textrm{d} x}\)</span> is the slope of the that solution curve. However, from (<a href="" class="xref" data-knowl="./knowl/eq1_6.html" title="Equation 1.3.1">(1.3.1)</a>), it can be seen that the slope is given by <span class="process-math">\(f(x, y)\text{,}\)</span> which is known. Thus, even if we do not know the solution curve, we still know its slope.</p>
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